Consider y = (1 + 3x²) Arctan x - 3. what is its derivative? %3D 1 +3x2 1 + x2 A - 6x Arctan x 1 +3x² 1 + x2 6x Arctan x 1 +3x2 1 + x2 + 3x Arctan x 1 +3x2 D 1 + x2 + 6x Arctan x Question 8 3x Evaluate lim ( tan sin - ). A 0 B 2 (c) does not exist B.

Q: Find the first derivative of 2cos(2 + x³). a. -6x² sin(2 + x³) b. -x² (sin 2 + x³) c. -6x² (cos…

A: daf(x)dx=adf(x)dx ; where , 'a' is constant. dcos (ax)dx =-a.sin(ax) dxndx=n.xn-1 .

Q: Find the derivative of f(x) =tan-1 (cos 6x) 6 sin 6x a. f'(x) = 1+cos? 6x - sin 6x b. f'(x) = 1+cos?…

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Q: [In(x²)-ex cos(x-1).tan(Tx) 20. lim 2x2-x sin2(1-x) X-1

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Q: - i) By using L'Hopital Rule, find sinx lim x-0 e3x 1 ii) Given that a = sin V3 2, find, csca -1

A: In L Hopital's rule take the derivative of numerator and denominator separately and than put the…

Q: Determine of y = cos(x) – V5a2 In x.

A: I have stated the used formulas in the solution.

Q: Differentiate: (etan(x)) /(1+x)  Show all working out.

A: Given  etanx1+x. We have to differentiate it. Used formula:- ddxfxgx=gx⋅ddxfx−fx⋅ddxgxgx2 Here,…

Q: What do the limits limh→0((sin h)/h) and limh→0((cos h - 1)/h) have to do with the derivatives of…

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Q: 1. Find the derivative. g(x)=(4x-2)^5-√(x^2+8)

A: We’ll answer the 1st question since we answer only one question at a time. Please submit a new…

Q: Find the derivative of g(x) = e * x). sin (1+ 0-3x²e*cos(1+x°) O xe*1sin(1+x°)+3x²e*cos(1+x) O…

A: The product rule of derivatives states that duv=u'v+v'u.

Q: What do the limits lim h-->0 ((sin h)/h) and lim h-->0 ((cos h - 1)/h) have to do with the…

A: Show the expression for derivative of sinx0  as follows:

Q: Discuss the relationship between the derivative dy/dx and (Lim) with drawing if it is required ?

A: See the attachment

Q: Find the critical points/number of the function h(x) = e^x sinx-sinx+cosx by applying derivatives.

A: First calculate its derivate then equate it equal to 0 to obtain the critical points. h(x)=exsin…

Q: Find the linearization of the function F(x)=tan-1(2x)= arctan(2x) at x=0. Then use linearization to…

A: We know the linearization of the function f(x) at x=a    L(x) = f(a) + f'(x)*(x-a)   In the…

Q: The first derivative of y=cos(tan(x2-7x+1)) is.. 1. O -[sin(tan(x²-7x+1))][sec²(2x-7)] 2. O…

A: Find the derivative of y=costanx2-7x+1

Q: limit x to 0 sin(4t)sec(1000t)/10t

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Q: If y = √√1-x² sin¹¹x, prove that (1-x²)+xy=1-x². dx

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Q: FInd the derivatives of the function f(x) from the first pribnciple  cos2x

A: Derivative from first principal is ratio of change in y to the very small chance in x.

Q: In(5æ) Find the derivative with respect to x of y = %3D 5x y' = | %3D

A: Find the derivative

Q: 7. The derivatives of the function f (x) = cos(3x²) that follow are incorrect. What misconception…

A: The differentiation of product two functions can be calculated by using the formula,…

Q: 1. If f(x) = sinx, show that f(x + y)-f(x) = cos x siny - 2 sin x sin² 2 2Y-T

A: 1) Given f(x)=sin(x)

Q: Compute Each Derivative: 1) d tan¯¹ (1 + e²x) dx 2) x²cos-¹(3x4) d dx 3) x(sin-¹(x))² dx

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Q: Lim as x approaches 0  1-cos(5x)+sin(3x)/x

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Q: 1- Find the equation of the tangent to the curve y = 2 sinx+ cos2x at the point x n. 2- Find the…

A: As per our guidelines we are supposed to answer only one question.Kindly repost other question as…

Q: Discuss the relationsh ip between the derivative dy/dx and(lim) with drawing if it is required

A: See the attachment

Q: Find the derivative of y with respect to x. y = 5x4 sin-1 r 1 V1-x? + 20x3 5x4 1+x2 + 20x³ sin¬1 x…

A: We have to find the derivative.

Q: What is the derivative of f(x) =2cos (x)? %3D 2 cos (2x) O -2 cos (2x) O 2 sin (2x) -2 sin (2x)

A: f(x) =2cos2xdifferentiating w.r.t xd(f(x))dx=ddx(2cos2x)

Q: Find the derivatives of the functions in Exercis

A: we have to find the derivative of the given function. g(t)=1+sin3t3-2t-1

Q: If f(x) = Α) B C D tanx sec ³x 1 + e tanx 1+tan²x 1+ e tanx sec²x 1+1² 1+e' -dt, then f'(x) equals…

A: We have to find derivative of given integral.

Q: Find the derivatives of the functions in Exercis

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Q: Find the derivative of the trigonometric function f(x)=x°t .5, °tanx. a. f'(x)=x°sec²x+ 5x*tanx b.…

A: Use the chain rule of derivative and simplify.

Q: 7. Find the derivative with respect to x of tan-(2) – In(2.r +3) = 4 cos (2y +5). %3D

A: To find the derivative of tan-1x2-ln2x+3=4cos32y+5. Solution: Power rule of differentiation states…

Q: Find dy/dx using appropriate derivative rules. 1. y = 8x^5/2 - 7x-9 + square root of 5 2. ) y =…

A: Since you have asked multiple questions in a single request, we will be answering only the first…

Q: 13. To evaluate f 2costx-1 dx, the integrand can be transformed to 1-sin²x a. [(3cos³x+csc²x)dx b.…

A: Here we have to transformed the given integrand.

Q: Find the first derivative of  y = cos4 x – sin4 x y = x3   –  x2 cos x  +  2x sin x  + 2 cos x y…

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Q: Find an expression for the derivative  dy/dx If  y=tan(x2sinh(x)) A) dy/dx =sec (x2 cosh(x) + 2x…

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Q: The derivative of sec² 2x (cos² r - sin² x) with respect to a is O2 sec 2x tan 2x O4 sec² 2x cot 2x…

A: Find the derivative

Q: |1- x 2 arctan + arcsin(2x – 1) = Hint using f Odx = C

A:

Q: Find all points with x-values on (0, 2π), where tangent line to the graph of f(x) is horizontal.…

A: Find all points with x-values on (0, 2π), where tangent line to the graph of f(x) is horizontal.…

Q: Find the derivative of f(x) = 2x(sinx)cos(x) ? a. f(x)=sin2x+2xcos2x b. f(x)=2sin2x+2xcos2x c.…

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Q: limit x to 0 3x-3xcox/sin^2(3x)

A: Here given limit as Use the L'hospital rule which states

Q: Find the derivative of f(x) = ecos² (3x+1) Of(z) 6 sin(3r+1) cos(3x + 1)ecos² (3+1) O (E) None of…

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Q: 11 tanto-2 tan Bz1 show that 2 coste- Cos B20

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Q: Find the derivative. 8) y = (x + 1)2(x2 + 1)-3 dy dx dy = -2(x + 1)(x2 + 1)-4(2x2 + 3x – 1) A) B) Y…

A: We can find the correct answer as below.

Q: Find the derivative of f(x) = 3r sin(-)(x) – In(r² – 1) + 8² – 5 cosh(x)

A: Find the derivative of function

Q: Find the partial derivative. xevllry ax

A: Given the function

Q: Use implicit differentiation with partial derivatives (as described in Example 4 page 732) to find…

A: Given function is, x2y+xy=4

Q: Find the function f(x) whose derivatives is sin x and whose graph passes through the point (0,2).…

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Q: limit x approaches zero, sin^2x/x

A: Given,